# Improved Land Evapotranspiration Simulation of the Community Land Model Using a Surrogate-Based Automatic Parameter Optimization Method

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## Abstract

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## 1. Introduction

## 2. Data and Methodology

#### 2.1. Data

#### 2.2. Systematic Parameter Optimization Framework

#### 2.2.1. Good Lattice Points (GLP) Uniform Sampling Method

_{1},…,h

_{s}) was first built, where h

_{i}(I = 1,…,s) were prime numbers lower than n, and h

_{i}≠ h

_{j}for i ≠ j. Then, the components of the sample were constructed as follows.

_{n}= {X

_{k}= (x

_{k1},…,x

_{ks}), k = 1,…,n} is called a lattice point set of the generating vector (n: h

_{1},…,h

_{s}). If the point set P

_{n}has the lowest discrepancy among all possible generating vectors.

#### 2.2.2. Multivariate Adaptive Regression Splines (MARS) Sensitivity Analysis Method

#### 2.2.3. Adaptive Surrogate Modeling-Based Optimization (ASMO) Parameter Optimization Method

- The perturbed parameter samples were obtained by sampling the sensitivity parameter adjustable ranges using the GLP sampling method. Then, these samples were put into the physical model (e.g., CLM4) instead of the default parameters, to obtain either the required model outputs (e.g., ET) or the output errors compared with observations. The perturbed parameters and their simulated outputs constituted the initial sample set.
- Based on the initial sample set, a statistical surrogate model was built between parameters and model outputs using the MARS regression method. Then, the traditional parameter optimization (e.g., the shuffled complex evolution (SCE-UA) global optimization method [23]) was used to search the optimal parameter values of the surrogate model.
- The optimal parameter values of the surrogate model were put into the physical model to obtain a new model output. As a new sample point, the optimal parameters of the surrogate model and their physical model output were added into the initial sample set.
- Steps 2 and 3 were repeatedly conducted until the convergence criterion was met. In this study, the convergence criterion was that the local optimal values remain unchanged after a number of searches equal to five or ten times the number of parameters.

#### 2.3. Model Setup

## 3. Results

#### 3.1. Sensitivity Analysis Results

#### 3.2. Sensitivity Parameter Optimization Results

#### 3.3. Comparison Analyses of Optimization Results

^{−1}) to southeastern (903.62 mm yr

^{−1}) China and, for observation, increased from northwestern (135.06 mm yr

^{−1}) to southeastern (944.72 mm yr

^{−1}) China. It showed that the CLM4 model was suitable for simulating ET in China. However, it was noted that significant differences occurred in the Tibetan Plateau region located in southwestern China.

^{−1}, which was lower than 122.89 mm yr

^{−1}for default ET simulations. Figure 5c shows that a significant difference occurs in the Tibetan Plateau, where the RMSE of default simulations is 208.98 mm yr

^{−1}. Figure 5d shows that the RMSE of ET simulations in the Tibetan Plateau is decreased to 183.73 mm yr

^{−1}when optimal simulations are used. Using the optimal parameters, the positive bias of ET simulations in the western parts of the Tibetan Plateau decreased from 127.39 to 95.73 mm yr

^{−1}. Correspondingly, the negative bias in the eastern parts of the Tibetan Plateau increased from −196.67 to −181.01 mm yr

^{−1}. Besides that, the ET simulation errors decreased from 67.18 to 56.83 mm yr

^{−1}in the northern region of China and from 82.64 to 60.63 mm yr

^{−1}in the mid-eastern regions of China. As a whole, these results demonstrated that the optimal parameters obtained by the ASMO method effectively improved the ET simulation of CLM4.

^{−1}in November. Besides that, there were weak negative improvements between January and May, and the range of loss errors was from 13.29 in January to 48.29 mm yr

^{−1}in February. It was also noted that the optimal simulations were smaller than the default simulations for all 12 months of the years 2009–2011, and the range of the difference between them is from 31.43 in March to 106.67 mm yr

^{−1}in October.

^{−1}) occurred in summer, followed by spring (468.27 mm yr

^{−1}) and fall (387.1 mm yr

^{−1}) and the minimum ET (147.81 mm yr

^{−1}) in winter. With the optimal parameters, the ET simulations in summer and fall were significantly improved and not improved in spring and winter. The ET improvement amount in summer was 49.67 mm yr

^{−1}, accounting for 6.14% of the summer observation, and in fall was 48.6 mm yr

^{−1}, accounting for 12.56% of the fall observation.

^{−1}in NNC to 90 mm yr

^{−1}in JH. Noted that ET simulation values after parameter optimization were still higher than observations.

^{−1}, accounting for 29.4% of SNC observations, and the JH subregion where the ET improvement amount was 147.51 mm yr

^{−1}, accounting for 25.44% of JH observations. The vegetation in the two subregions is mainly deciduous broadleaf forest. For the TP subregion, the ET improvement was insignificant, which may be caused by the offset of the positive and negative deviation between the East and West of the TP. In winter, the improvements of the ET simulations mainly occurred in the subregions of the north of China with the smaller ET values. Therefore, the improvement effect was very weak. For the subregions of the south of China, SE and SW had obvious negative improvements, except for JH, with a 14.36% improvement in the absolute value error. Thus, the overall ET simulation was not improved. In addition, it was noted that these improvement rates were not comparable, because their referred observation values were different.

#### 3.4. Validation Analyses of Community Land Model Version 4.0 Optimal Parameters

#### 3.5. Comparisons between Default and Optimal Parameters

_{y}(fraction of water volume that is drained by gravity in an unconfined aquifer) and poro_b (the intercept of mineral soil porosity pedotransfer functions) were higher than the default values. The opposite variations occurred in the parameters fdrai (decay factor of subsurface flow), suc_b (the intercept of pedotransfer functions of saturated mineral soil matric potential), z0mr (ratio of momentum roughness length to canopy top height), rholnir (leaf reflectance: near-infrared radiation), and taulnir (leaf transmittance: near-infrared radiation).

## 4. Discussion

_{y}(i.e., P4) are two of the sensitive parameters in the simulations of soil evaporation and transpiration shown in Figure 3. Hou et al. [28] reported that when fdrai < 2, it is directly proportional to the amount of simulated ET. Therefore, the lower fdrai value in Figure 11 would be expected to decrease the default simulated ET amount. In a physical sense, fdrai is related to drainage in the CLM4 model, such that lower fdrai values correspond to increased drainage. As a result, more water in shallow aquifers recharges the groundwater downward, leading to a decrease of soil water and, consequently, lower soil evaporation and transpiration.

_{y}(specific yield) represents the volumetric proportion of water in the soil that is free to move by gravity. When S

_{y}increases, more free water is generated in shallow aquifers. Under the action of gravity, the increased volume of free water recharges the underlying aquifer and, thus, has the same effect as the fdrai value discussed above.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The study domain and its eight subregions marked with blue boxes. The eight subregions are (

**I**) northeastern (NE, 40°–50° N, 120°–135° E), (

**II**) northern part of North China (NNC, 41°–45° N, 110°–120° E), (

**III**) southern part of North China (SNC, 35°–41° N, 110°–120° E), (

**IV**) northwestern (NW, 36°–45° N, 75°–110° E), (

**V**) Tibetan Plateau (TP, 28°–36° N, 80°–101° E), (

**VI**) southwestern (SW, 24°–36° N, 101°–110° E), (

**VII**) Jianghuai region (JH, 30°–35° N, 110°–122° E), and (

**VIII**) southeastern (SE, 22°–30° N, 110°–120° E).

**Figure 2.**Monthly variation of the evapotranspiration (ET) observation and simulations from 2009 to 2011 in China: (

**a**) total evapotranspiration observation and simulation; and (

**b**) simulations of evapotranspiration’s three components, including soil evaporation, canopy evaporation, and transpiration.

**Figure 3.**Normalized sensitivity scores of 38 parameters for total evapotranspiration and its three component simulations. MARS = multivariate adaptive regression spline method.

**Figure 4.**Optimization speed for evapotranspiration simulation in Community Land Model version 4.0 using the adaptive surrogate modeling-based optimization method.

**Figure 5.**Comparisons of the spatial distribution of evapotranspiration simulations from 2009 to 2011 over China using Community Land Model version 4.0 model with default and optimal parameters: (

**a**) observations. The white grids in China represent the missing values, (

**b**) default simulations, (

**c**) bias of default simulations minus observations, and (

**d**) bias of optimal simulations minus observations.

**Figure 6.**Comparisons between mean monthly evapotranspiration simulated values for 2009–2011 using Community Land Model version 4.0 model with default and optimal parameters for: (

**a**) total evapotranspiration, (

**b**) soil evaporation, (

**c**) canopy evaporation, and (

**d**) transpiration.

**Figure 7.**Comparisons of evapotranspiration simulations using default parameters and optimal parameters in the eight subregions of China.

**Figure 8.**Comparisons of the evapotranspiration at the seasonal scale among default simulations, optimal simulations, and observations for China and its eight subregions for: (

**a**) Spring, (

**b**) Summer, (

**c**) Fall, and (

**d**) Winter.

**Figure 9.**Comparisons of the spatial distribution of evapotranspiration simulations from 2014 to 2015 over China using Community Land Model version 4.0 model with default and optimal parameters: (

**a**) observations. The white grids in China represent the missing values, (

**b**) default simulations, (

**c**) bias of default simulations minus observations, and (

**d**) bias of optimal simulations minus observations.

**Figure 10.**Comparisons of evapotranspiration simulations using default parameters and optimal parameters in the eight subregions of China. 2014–2015.

**Figure 11.**Comparisons of normalized optimal and default parameter values of Community Land Model version 4.0 model for the evapotranspiration simulations in China.

**Table 1.**List of sensitive parameters for the evapotranspiration simulation in the Community Land Model version 4.0.

Index | Parameter | Default | Range | Description |
---|---|---|---|---|

P2 | fdrai | 2.5 | (0.1, 5) | Decay factor of subsurface flow (m^{−1}) |

P4 | S_{y} | 0.2 | (0.02, 0.27) | Fraction of water volume drained by gravity in an unconfined aquifer |

P6 | poro_b | 0.489 | (0.4401, 0.5379) | The intercept of mineral soil porosity pedotransfer function |

P10 | suc_b | 1.88 | (1.692, 2.068) | The intercept of pedotransfer function of saturated mineral soil matric potential |

P16 | z0mr | 1 | (0.7, 1.3) | Ratio of momentum roughness length to canopy top height |

P32 | rholnir | 1 | (0.7, 1.3) | Leaf reflectance: near-infrared radiation |

P36 | taulnir | 1 | (0.7, 1.3) | Leaf transmittance: near-infrared radiation |

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**MDPI and ACS Style**

Zhang, C.; Di, Z.; Duan, Q.; Xie, Z.; Gong, W.
Improved Land Evapotranspiration Simulation of the Community Land Model Using a Surrogate-Based Automatic Parameter Optimization Method. *Water* **2020**, *12*, 943.
https://doi.org/10.3390/w12040943

**AMA Style**

Zhang C, Di Z, Duan Q, Xie Z, Gong W.
Improved Land Evapotranspiration Simulation of the Community Land Model Using a Surrogate-Based Automatic Parameter Optimization Method. *Water*. 2020; 12(4):943.
https://doi.org/10.3390/w12040943

**Chicago/Turabian Style**

Zhang, Chong, Zhenhua Di, Qingyun Duan, Zhenghui Xie, and Wei Gong.
2020. "Improved Land Evapotranspiration Simulation of the Community Land Model Using a Surrogate-Based Automatic Parameter Optimization Method" *Water* 12, no. 4: 943.
https://doi.org/10.3390/w12040943